Leonard Euler
A
Mathematician
For all
Seasons
By A Chaparral High School
Teacher
Leonhard Euler
lived from 1707 to 1783
Euler made large bounds in modern analytic
geometry and trigonometry. He made decisive
and formative contributions to geometry, calculus
and number theory.
Euler was born in
Basel, Switzerland on
April 15, 1707
What do we know about Switzerland?
•Full country name: Swiss Confederation
•Area: 41,295 sq km (16,105 sq mi)
•Population: 7.3 million
•Capital city: Bern (pop 130,000)
•People: 74% German, 20% French, 4% Italian & 1%
Romansch
•Language: German, French, Italian & Romansch
•Religion: 49% Roman Catholic & 48% Protestant
Since the dominant language is German, can
you guess how his name is pronounced?
(to hear his name correctly pronounced click here )
You heard right, “Oiler”!
Euler:
• His father wanted his son to follow him into
the church and sent him to the University of
Basel to prepare for the ministry.
• He entered the University in 1720, at the
age of 14, first to obtain a general education
before going on to more advanced studies.
• Johann Bernoulli soon discovered Euler's
great potential for mathematics in private
tuition that Euler himself engineered.
. Euler's own account given in his
unpublished autobiographical writings, is
as follows:-
... I soon found an opportunity to be introduced to a
famous professor Johann Bernoulli… True, he was
very busy and so refused flatly to give me private
lessons; but he gave me much more valuable advice to
start reading more difficult mathematical books on my
own and to study them as diligently as I could; if I
came across some obstacle or difficulty, I was given
permission to visit him freely every Sunday afternoon
and he kindly explained to me everything I could not
understand ...
•In 1723 (at the age of 16) he completed his Master’s
degree.
•He finished his studies within the next few years.
•In 1727 he began teaching at the St. Petersburg
Academy of Sciences.
•He became professor of physics in 1730
•He became senior chair of mathematics in 1733
In 1738 he lost the sight in his right eye.
Euler’s comment upon this occurance is stated to be:
"Now I will have less distraction."
• Euler was director of mathematics and
physics in the Berlin Academy from 1741-
1766 (when he lost the sight of his other
eye).
• He published over 800 different books and
papers on pure and applied mathematics,
physics and astronomy.
NOW…………..
Let’s look at some of Euler’s
accomplishments!
There is a town in Russia whose name today is Kaliningrad.
In the 1700s, it was in Prussia and its name was Königsberg.
Here's a true story.
Once upon a time (OK, in the 18th century), in a place
far away (well, Prussia), there once was a town called
Königsberg. The townspeople enjoyed walking through
their town and passing over the seven bridges
spanning the river which passed through town. Over
the years, a controversy arose and eventually word of it
reached Euler…
The problem is stated as follows: In the town of Königsberg in
Prussia there is an island called Kneiphhof, with the two branches
of the river Pregel flowing around it. There are 7 bridges crossing
the two branches. [as shown below] The question is whether a
person can plan a walk in such a way that he will cross each of
these bridges once but not more than once.
So, what did he find out?
• It was impossible to do that!
• Euler went on to formulate a general
theory which solved this particular
problem and created a new branch of
mathematics called graph theory.
• To find out more try:paths
•Euler contributed to every mathematical field that existed
at the time. He standardized modern mathematics notation
when he used symbols such as f(x), e, i and sin(x). He
was the first person to represent trigonometric values as
ratios and prove that e is an irrational number.
•His invention of the calculus of variations led to the
general method to solve maximum and minimum value
problems.
•He was also one of the first people to recognize that
infinite series had to be convergent to be used safely.
•In physics, he developed the general equations for
hydrodynamics and for motion.
Possibly his most impressive work was his
approximation of the three-body problem of the
sun, earth and moon, which he solved while
completely blind and performing all the
computations in his head.
WOW!
. Euler was able to relate the number of faces
(F), vertices (V) and edges (E) of a polyhedron
by the following equation,
F+V=E+2
from which one can derive that there are only
five regular polyhdera.
In fact, Germany created a stamp
that commemorates this formula
discovery:
Euler also discovered the formula
• eix = cos x + i sin x
Which happens to be commemorated on a Swiss stamp:
Euler’s importance to society is reflected in his appearance
not just on stamps but on currency as well!
So, as you can see Euler’s contributions to
mathematics are broad and varied. His impact
can still be felt in algebra, geometry, calculus
and other branches of mathematics such as
topology and graph theory.
Indeed, it is difficult to find a mathematician,
modern or historical, who was as prolific as
Leonhard Euler,
but I challenge you to try!
Project Assessment: PowerPoint Presentation
Layout (15 points possible)
q Is your presentation easy to view and attractive? (6 points)
q Does your presentation avoid clutter yet utilize the space on the slide? (3 points)
q Are slide transitions used appropriately? (3 points)
q Are graphics, animations, sounds, and other multimedia used for a purpose? (3 points)
Organization (15 points possible)
q Do titles and other important elements stand out on the slide? (3 points)
q Do slides progress in a logical order? (3 points)
q Do elements of slides appear in the proper order? (3 points)
q Are bullets or other organizing aids used appropriately? (3 points)
q Are there appropriate title, outline, and conclusion slides? (3 points)
Content (15 points possible)
q Does your presentation effectively summarize important information? (3 points)
q Are words spelled correctly and is grammar used properly? (3 points)
q Does your show contain at least 10 content slides? (3 points)
q Does your presentation contain at least 5 multimedia images, sounds, animations,
videos, etc.? (3 points)
q Is author and source information included? (3 points)
Classroom Presentation (5 points possible)
q Is the pace of your presentation a comfortable one for your audience? (3 points)
q Do the presenters speak clearly, confidently, and with appropriate eye contact? (2
points)
TOTAL (50 points possible)